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JOURNALS // Proceedings of the Yerevan State University, series Physical and Mathematical Sciences // Archive

Proceedings of the YSU, Physical and Mathematical Sciences, 2024 Volume 58, Issue 2, Pages 47–56 (Mi uzeru1095)

Mathematics

Vertex distinguishing proper edge colorings of the corona products of graphs

T. K. Petrosyan

Russian-Armenian University, Institute of Mathematics and Informatics, Yerevan

Abstract: A proper edge coloring of a graph $G$ is a mapping $f:E(G)\longrightarrow\mathbb{Z}_{\geq 0}$ such that $f(e)\not=f(e')$ for every pair of adjacent edges $e$ and $e'$ in $G$. A proper edge coloring $f$ of a graph $G$ is called vertex distinguishing, if for any different vertices $u,v \in V(G)$, $S(u, f) \ne S(v, f)$, where $S(v, f) = \{f(e) \ | \ e = uv \in E(G)\}$. The minimum number of colors required for a vertex distinguishing proper coloring of a graph $G$ is denoted by $\chi'_{vd}(G)$ and called vertex distinguishing chromatic index of $G$. In this paper we provide lower and upper bounds on the vertex distinguishing chromatic index of the corona products of graphs.

Keywords: edge coloring, proper edge coloring, vertex distinguishing proper coloring, corona product

MSC: Primary 05C15; Secondary 05C76

Received: 02.09.2024
Revised: 21.09.2024
Accepted: 02.10.2024

Language: English

DOI: 10.46991/PYSU:A.2024.58.2.047



© Steklov Math. Inst. of RAS, 2025